The Blaugrana last month confirmed the signing of the Brazil international from Santos for a fee of €57 million (£50m) and great things are expected of the 21-year-old, particularly in light of his subsequent stellar showings for the Selecao at the Confederations Cup.
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"He will adapt very quickly," the Spain star told El Mundo Deportivo. "It is true that you need an adjustment period to get to know the game in another country: how everything is, the city etc.
"But, like I said, I think he will adapt fairly quickly. He has very good friends there, such as Dani Alves and Adriano, and that will help.
"I think he is also happy and excited about playing for Barca, so hopefully be an important player for us."
Johan Cruyff has suggested that the Catalans should cash in on Lionel Messi now that they have acquired Neymar, but Pedro can see no reason why they would allow the four-time Ballon d'Or winner to leave.
"He is the best in the world," the winger enthused. "It is a privilege and a pleasure to have him with us.
"This is demonstrated in every game and it's amazing. You cannot compare any player in the world today with Messi."
As for his own future at Camp Nou, Pedro revealed that, despite the increased competition for places at Camp Nou, he would like to spend the rest of his career with the club.
"I want to continue at Barca many years - and I hope to," he admitted.
"I know it's difficult because Barca will always demand a lot - you always have to play at the highest level - but the truth is that today I only think about the national team and Barca."